Question

How do you write an equation that contains points (-1, 2) and is parallel to x-2y=-3?

Answer 1

`1x-2y=-6`

Explanation:

All lines parallel to `x-2y= -3` will have the same slope as `x-2y=-3`

That is all lines parallel to `x-2y=-3` will have a slope `m=1/2` (see below if the reason for this isn't obvious)

Using the slope point form (with point `(hatx,haty)=(-1,2)` and slope `m=1/2`)
we have
`color(white)("XXXX")(y-2)=1/2(x-(-2))`
which we could simplify as
`color(white)("XXXX")2y-4= x+2`
or in standard form as
`color(white)("XXXX")1x-2y = -6`

further explanation
How do we know the slope of `x-2y=-3` has a slope of `1/2`?

We can rearrange `x-2y=-3` as
`color(white)("XXXX")-2y= -x-3`
or
`color(white)("XXXX")y =1/2x + 3/2`
which is ane equation in slope-intercept form
with a slope of `1/2`
(and a y-intercept of `3/2`, although this isn't relevant to this question)